I'm really surprised this wasn't answered when it was posted on the Day of the Dead event, as his burocratiship Giovanni Alvise Falier was keeping an eye on the answers (but I suppose he didn't really understand how the Refresh button worked, and besides, he was terrified at the prospect of how much paperwork something like a computer would eliminate).

All the better, as Alvise would probably have spent more time explaining how prestigious and important the order was while being vague on specifics lest his descriptions give any dangerous ideas to newly ennobled dynasties from Candia (modern Crete) which in the 1660s were rapidly migrating to the Venetian capital to escape the conflict on their home island. Alvise, a middling member of an ancient dynasty, would have perceived his privileges to be threatened by these new admittees (what with their achievements and skills).

The late 16th century had seen several changes in chivalrous orders in Venice, and these changes would be transmuted as the Venetians' own notions of aristocracy changed in centuries that followed. Venetian officers serving foreign armies, and foreign veterans settling in Venice, had created a demand for recognition of titles and awards accumulated during conflicts like the Italian Wars. Previously, the mostly flat Venetian aristocracy had been disinterested in titles of any kind (any aristocrat wearing arms and armor was a "Milites Nobili without anyone having pinned a medal on them) however as economic prosperity waned and social strata solidified, prosperous Venetians looked for new ways to differentiate themselves. This was exacerbated by the loss Venetian overseas possessions: while the trade routes passing through places like Crete and Negroponte didn't disappear altogether, ethnic Italians permanently living on Greek Islands saw fewer and fewer reasons to stay year-round (if at all). As a way to pacify a potentially restless portion of the population, and perhaps to strengthen a political faction in favor of war-taxes (much like the Republic looking to recover colonies, these colonies' inhabitants were hoping to recover properties the Venetian retreat had forced them to abandoned in the Aegean) the most prosperous of these "Venetian Greeks" were admitted to the aristocracy. This created a further demand for honors and titles, as on the one hand ancient Venetian dynasties sought to flaunt their privileges and connections (especially if there were dynasty members with little else going for them) while these "new" dynasties sought to obtain recognition for their military and civil service to the Republic.

Similarly, as relations with the Ottoman Empire soured over the course of the 17th century on the one hand the Venetians fought tooth-and-nail to keep their overseas outposts, but on the other the Republic's leadership also felt that with the East causing nothing but trouble a strengthened desire developed to align itself with Western Europe. Indeed, it is undeniable that in the previous century, the Italian Wars and the growth of Atlantic trade had worked to end the Venetian's notion that they were an eastern capital transmuted west by pure happenstance. Thus a game of catch-up began by which the Venetian aristocracy and government sought to align themselves with the part of the continent they chose to be their peers.

And here, after this long preamble to explain why there even were knightly orders in Venice in the first place, we can look at how this trend actually materialized: The first official knightly order in Venice was the Order of Saint Mark, created sometime in the fifteenth century to give foreigners serving the Republic an honor on par with the sort of knighthoods they would expect to receive abroad. The Venetians didn't really take to formalizing their knightly orders however, as the Senate was happy to continue awarding lands and stipends on an ad-hoc basis as it had always done, seldom tacking on a knighthood. Again, for the Venetian Aristocracy which was still mostly flat at this point, Great Council and its members (consisting of all ennobled male residents of Venice) only really cared about political representation, and were disinterested in titles.

My long-winded preamble on social conditions in Venice is also important as once the 16th century saw social stratification become more evident, a desire arise to recognize the inverse achievement to the Order of St. Mark: this is the incipit of the Order of the Golden Sole. Any Venetian who had been awarded a foreign knightly honor was added to the rolls of the Order of the Golden Stole on confirmation by the Venetian senate. The order was typically applied to former ambassadors, who wanted to formalize titles they had earned while living abroad.

Alvise, however, has been the beneficiary of a shift taking place in the 17th century, where admission to the order by the Senate began being used as a presumption of the accumulation of foreign titles, a further testament to social stratification. In fact, even as a middling member of the Faledri dynasty, Alvise could expect to be tapped to accompany a more high-profile relative to on a mission or appointment abroad (although ambassadors were typically selected among those Venetians who were already living abroad, on the accumulation of additional responsibilities like an ambassadorship would generate a need to send for trusted collaborators; a running joke I had intended to include in my Day of the Dead answers as Alvise Falier would have been be his description of attempts to extricate himself from the requests of more successful relatives living abroad, and the rather feckless and vain character I had built around Alvise Falier would have accepted the honor without understanding it was a presumption he would then accept a posting abroad).

Apart from social signaling, the Knightly Order of the Golden Stole seems to have been mostly a social marker with few, if any, practical privileges. For the cosmopolitan and well-traveled Venetian aristocracy, the most important concession would have probably been the ability to keep using any and all titles accumulated while living abroad (not only marking them as desirable social acquaintances, but also as desirable business partners who could be presumed to have extensive foreign contacts). However not all Venetians cared to apply in order to wear their foreign medals, and even those that did ask were only granted admittance on the condition they renounce some or other element of their foreign knightships (awards like ceremonial arms and armor were things the senate was least willing to allow, and even foreign knights would be strongly discouraged from wearing ceremonial martial dress in public right to the Republic's final decades)

The Stole itself also seems to have been somewhat underwhelming: a cloth sash that was bordered with golden thread. Again, the more impressive distinction would have been the ability to wear foreign medals, as well as the red ceremonial robes that were typically only reserved for the highest officers of the Republic (for a middling bureaucrat, this would have been a great draw for Alvise who would be wearing the same robes as the Savi he served).

Risi e Bisi, to get to your second question, was a fairly popular late-winter or early-spring dish available in Venice since the absorption of the mainland city of Vicenza in the first decade of 15th century. Peas, which are a hardy Mediterranean vegetable that can be planted in October or November to be ready for March or April, were cultivated in the Vicentine hills starting from at least the 10th century (especially in the vicinity of Lumignano). While Risi e Bisi were and are a springtime staple of all of the lower northeast, in Alvise's time they would have been most famous as the meal served in the Doge's banquet hall on St. Mark's Day (the 25th of April). The dish, which has a soupy-er consistency than other kinds of risotto, is well-suited for serving to a large group of people as the Doge's servants would certainly have had to.